select_next_item() work only with history selection?
Using vert[0].select=True doesn't add the vertex to the bmesh select history, you need to add it yourself.

vert[0].select=True
bm.select_history.add(vert[0])
vert[1].select=True        
bm.select_history.add(vert[1])


You may notice that the select history doesn't include all selected items, if you Alt-Click to select an edge loop only one vertex (the active vertex which was closest to the click) is added to the history. Shift-Alt-Click will then add a second vertex which is the new active vertex. If you use select all then nothing is in the history.